Pour the root beer into a large saucepan and heat over moderate flame. Bring to a boil and reduce to 1.5 cups.
Combine the gelatin and cold water in the bowl of stand mixer. Allow to bloom while you prepare the sugar syrup.marshmallows
Combine root beer syrup, corn syrup, and sugar in a small saucepan. Bring to a boil over medium heat, stirring occasionally.
With the mixer on low, slowly pour the boiling syrup into the gelatin, then turn to high and whip for 10 minutes. Add salt and extract and whip just enough to incorporate.
Transfer marshmallow to a 13x9 pan lined with greased parchment paper. Lay a piece of greased plastic wrap on top and press into a uniform slab. Place in refrigerator to set for three hours, then cut into 1.5 inch cubes. Toss in powdered sugar if desired.